Simplify (x-8)/(x^2-3x-40)*(x^2-25)/(x+9)

$\frac{x - 8}{x^{2} - 3 x - 40} \cdot \frac{x^{2} - 25}{x + 9}$

Step 1

Factor $x^{2} - 3 x - 40$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 40$ and whose sum is $- 3$ .

$- 8, 5$

Write the factored form using these integers.

$\frac{x - 8}{(x - 8) (x + 5)} \cdot \frac{x^{2} - 25}{x + 9}$

Step 2

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{x - 8}{(x - 8) (x + 5)} \cdot \frac{x^{2} - 5^{2}}{x + 9}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{x - 8}{(x - 8) (x + 5)} \cdot \frac{(x + 5) (x - 5)}{x + 9}$

Step 3

Simplify terms.

Cancel the common factor of $x + 5$ .

Factor $x + 5$ out of $(x - 8) (x + 5)$ .

$\frac{x - 8}{(x + 5) (x - 8)} \cdot \frac{(x + 5) (x - 5)}{x + 9}$

Cancel the common factor.

$\frac{x - 8}{(x + 5) (x - 8)} \cdot \frac{(x + 5) (x - 5)}{x + 9}$

Rewrite the expression.

$\frac{x - 8}{x - 8} \cdot \frac{x - 5}{x + 9}$

Multiply $\frac{x - 8}{x - 8}$ by $\frac{x - 5}{x + 9}$ .

$\frac{(x - 8) (x - 5)}{(x - 8) (x + 9)}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{(x - 8) (x - 5)}{(x - 8) (x + 9)}$

Rewrite the expression.

$\frac{x - 5}{x + 9}$

Simplify (x-8)/(x^2-3x-40)*(x^2-25)/(x+9)

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